Modified continuum theoretical model for size-dependent piezoelectric properties of nanowires

In this paper, a continuum theoretical model for interpreting size-dependent piezoelectric properties of nanowires is proposed. The influence of surface elasticity and surface piezoelectricity decreases with increasing distance from nanowire surface. The decrease law is considered as exponential in this work. Core-surface model and core-shell model divide a nanowire into surface area and bulk like core. Since a nanowire is same material for surface area and bulk like core, the change law of elasticity and piezoelectricity should be identical within these two areas. Therefore, there should not be substantive difference between surface area and bulk like core. The corresponding interface is also gone in this train of thought. Due to the influence of surface elasticity and surface piezoelectricity, the nonlinear and exponential surface modifications for Young's modulus as well as piezoelectricity are introduced. The applications of the current theory to ZnO nanowire Young's modulus, ZnO piezoelectric coefficient and GaN piezoelectric coefficient give good agreement.